Are you saying that this redshifting is detectable on earth ? So they knew the signal came from a planet where time goes much much slower ? So they knew they received a signal that had been emitted for only 5 real minutes ? Are those questions "question worthy" or not ?

Yes, the amount of redshift as the signal climbs out of the gravity well should be the same as the redshift seen by arbitrarily distant observers, so unless the wormhole further adjusts the frequency significantly (which I suspect it wouldn't since it doesn't have intense gravity), this should be the same redshift seen on Earth. Whether they would know the time dilation factor would depend on whether Dr. Miller had only one available frequency to transmit at, or if she could pick a higher transmitter frequency based on knowledge of the redshift factor.

What I meant was that the received the message. But the message was dilated (redshifted), right ? In my mind, instead of receiving "good planet, ping" they receive something like "gooooood plaaaaneeeeeeet, piiiiiiing" so they must realize there is something wrong. Because their transmitter can't make the adjustment automatically, right ?

I'm just saying we don't know what the transmitter can do--seems quite possible that it can both adjust the frequency and the speed at which 1's and 0's making up the message are sent.

Yes, but if it does so, it would be ridiculous if the NASA couldn't detect it. I mean from an engineer point of view, having some device take some liberty (like automatically adjusting a signal) without warning you seems dumb. That's why I find it hard to believe the NASA couldn't detect that this planet was in a time dilated environment.

NASA may not have been expecting any very significant degree of time dilation, it was an incredibly unusual situation even by the standards of black holes (rotating much closer to the maximum possible rate than astrophysicists expect is likely). If the receiving devices were scanning a particular expected frequency, and looking for a meaningful message consisting of some series of bits the devices expected to be on/off signals lasting a characteristic amount of time, then Dr. Miller might want to adjust the transmitter just to make sure the receiving devices would actually pick it up.

I'm sorry, your "if" is a bit long and I don't understand it, I don't speak english perfectly :/

Well, which part do you want me to clarify? I was saying that if we assume that:

A) The receiving devices were scanning a particular expected frequency

B) The receiving devices were looking for a message consisting of some series of bits, which the receiving devices expected to be on/off signals that lasted for a characteristic amount of time

THEN, if A) and B) are how the receivers are programmed to work, Dr. Miller would probably want to adjust the signal she sent to give the receivers the type of message they were "expecting".

oh I see

well

When they go on the ice planet

the doctor says something like "I knew I just had to push a button for someone to come and save me"